System and method for reducing critical current or magnetic random access memory

ABSTRACT

A system and a method for reducing critical current of magnetic random access memory (MRAM) are disclosed. The magnetic device includes at least a pinned layer, a spacer layer and a free layer, and the material of the pinned layer and the free layer is perpendicularly anisotropic ferrimagnetic. The spacer layer is an insulator. By the modified Landau-Lifshitz-Gilbert equations, the varying trend of the critical current can be estimated.

RELATED APPLICATIONS

This application is a Divisional/Continuation patent application ofco-pending application Ser. No. 11/645,550, filed on 27 Dec. 2006. Theentire disclosure of the prior application Ser. No. 11/645,550, fromwhich an oath or declaration is supplied, is considered a part of thedisclosure of the accompanying Divisional/Continuation application andis hereby incorporated by reference.

BACKGROUND

1. Field of Invention

The present invention relates to a system and a method for reducingcritical current of magnetic random access memory, and more particularlyto a system and a method for reducing critical current of a magneticdevice with perpendicularly anisotropic ferrimagnetic structure.

2. Description of Related Art

Most magnetic memory devices employ magneto resistance of in-the-planemagnetic elements for storing data. For example, Magnetic Random AccessMemory (“MRAM”) is a kind of non-volatile memory utilized for datastorage. MRAM devices offer low power consumption and high reliability.In addition, MRAM devices can have a higher density memory device arraythan other conventional storage devices.

Reference is made to FIG. 1 a and FIG. 1 b, which show a conventionalmagnetic memory device 100. The magnetic memory device 100 includes anantiferromagnetic layer 110, a pinned layer 120, a spacer layer 130 anda free layer 140.

The antiferromagnetic layer 110 is used to fix, or pin, themagnetization of the pinned layer 120 in a particular direction. Thepinned layer 120 and the free layer 140 are ferromagnetic with amagnetization 121 and 141 in the plane, respectively. The spacer layer130 is a nonmagnetic insulator. The magnetization 141 of the free layer140 is free to rotate, typically in response to an external field.

FIG. 1 a shows the magnetization 121 and 141 as parallel in the samedirection. In this configuration, the magnetic resistance of themagnetic random access memory 100 is in a lower state. FIG. 1 b showsthe magnetization 121 and 141 as parallel in opposite directions, andthe magnetic resistance of the magnetic random access memory 100 is in ahigher state.

A conventional method for changing the direction of the magnetization ofthe free layer is to apply two orthogonal currents to the magneticdevice, for example, the X-Y selection mechanism. The method applies twoorthogonal currents as read and write currents of each magnetic device.Thus, either a definite volume of each magnetic device is required, orthe adjacent magnetic device in the memory device array is affected bythe read or write current.

However, there are some disadvantages in the conventional magneticdevice. For example,

1. The conventional magnetic device needs an antiferromagnetic layer tofix the pinned layer's magnetization; the manufacturing process is morecomplicated.

2. The known method of changing the magnetization direction limits thedensity of the magnetic device array, thus raising power consumption.

SUMMARY

It is therefore an objective of the present invention to provide asystem that can be a magnetic random access memory, which appliesperpendicularly anisotropic ferrimagnetic material to form the pinnedlayer and the free layer. There is no need for the additionalantiferromagnetic layer of the prior art to fix the pinned layer. Unlikethe prior art, the magnetization of the pinned layer and the free layerare perpendicularly anisotropic, so the volume of the magnetic device ofthe present invention can be smaller than the known one.

It is another objective of the present invention to provide a method forreducing critical current of the magnetic random access memory. Themethod employs a modified Landau-Lifshitz-Gilbert (LLG) equation thatincludes spin transfer effect to simulate the variation of criticalcurrent value.

According to the aforementioned objectives of the present invention, amagnetic system is provided. In one embodiment of the present invention,the magnetic system includes a pinned layer, a spacer layer and a freelayer. The pinned layer is the base layer of the magnetic system, andthe free layer is the top layer. The material of the pinned layer andthe free layer are ferrimagnetic, and both of the magnetizations areperpendicularly anisotropic, wherein the magnetization of the free layeris free to rotate. The spacer layer is between the pinned layer and thefree layer, and the material of the spacer layer is insulating material.

The magnetization precession and switching (i.e. rotation) of the freelayer is induced by the spin transfer torque of spin-polarized current,and the positive/negative spin-polarized current passes through themagnetic system's sandwich structure, which means the electrons flow upor down.

In accordance with the foregoing and other objectives of the presentinvention, a method for reducing critical current is provided. A finalequation via the modified LLG equation is obtained to describe thedynamics of net magnetization. The final equation shows the timeevolution of net magnetization under the influence of a spin-polarizedcurrent, as well as the estimation of the critical current for thepractical application in MRAM writing.

Because the different spin-polarized currents have distinct spinorientations, individual critical current and current density values areobtained. Finally, the varying trend of the critical current is given.

It is to be understood that both the foregoing general description andthe following detailed description are by examples and are intended toprovide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification. The drawings illustrate embodiments of theinvention and, together with the description, serve to explain theprinciples of the invention. In the drawings,

FIG. 1 a illustrates a prior art magnetic device whose magnetizationsare parallel;

FIG. 1 b illustrates a prior art magnetic device whose magnetizationsare antiparallel;

FIG. 2 illustrates a magnetic random access memory of the preferredembodiment of the present invention;

FIG. 3 illustrates a spin-polarized current applied to a magnetic systemof the preferred embodiment of the present invention;

FIG. 4 a illustrates the spin orientation of the spin-polarized currentapplied to the magnetic system (θ=0);

FIG. 4 b illustrates the spin orientation of the spin-polarized currentapplied to the magnetic system (θ=π/2);

FIG. 4 c illustrates the spin orientation of the spin-polarized currentapplied to the magnetic system (θ=π); and

FIG. 4 d illustrates the spin orientation of the spin-polarized currentapplied to the magnetic system (θ=3π/2).

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Reference is now made in detail to the present preferred embodiments ofthe invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers are used in thedrawings and the description to refer to the same or like parts.

While the specification concludes with claims defining the features ofthe invention that are regarded as novel, it is believed that theinvention is better understood from a consideration of the followingdescription in conjunction with the figures, in which like referencenumerals are carried forward.

First Embodiment

Reference is made to FIG. 2, which illustrates a magnetic memory randomaccess memory of the preferred embodiment of the present invention. Amagnetic random access memory 200 includes a pinned layer 210, a spacerlayer 220 and a free layer 230.

The pinned layer 210 is a base layer of the magnetic random accessmemory 200. The material of the pinned layer 210 may be a ferrimagneticthin film, such as TbFeCo alloy, DyFeCo alloy, Co/Pt multilayer thinfilm, Co/Pd multilayer thin film, or other ferrimagnetic multilayer thinfilm. A dipole moment 211 and a dipole moment 212 are perpendicularlyanisotropic and represent a definite strength, form a net magnetizationof first layer 213.

The spacer layer 220 is a nonmagnetic layer, which is an insulator. Thefree layer 230 is a top layer of the magnetic random access memory 200.The material of the free layer 230 could be a ferrimagnetic thin film,such as TbFeCo alloy, DyFeCo alloy, Co/Pt multilayer thin film, Co/Pdmultilayer thin film, or other ferrimagnetic multilayer thin film. Ifthe free layer 230 is a TM-rich (Transition Metal; TM) material, whereina component of a magnetization 231 and a component of a magnetization232 form a net magnetization of second layer 233; if the free layer 230is a RE-rich (Rare Earth; RE) material, wherein a component of amagnetization 234 and a component of a magnetization 235 form a netmagnetization of second layer 236, which are perpendicularly anisotropicand free to rotate; namely, the net magnetization of second layer 233and the net magnetization of second layer 236 may form an included anglewith the direction normal to the layers.

The thickness of the pinned layer 210 is 0.5 to 100 nm. The thickness ofthe spacer layer 220 is 0.5 to 10 nm. The thickness of the free layer230 is 0.5 to 100 nm. The thickness and the composition of every layercan be modulated to change their magnetic and electric properties.

Second Embodiment

Reference is made to FIG. 3, which illustrates a spin-polarized currentapplied to the magnetic memory device of the preferred embodiment of thepresent invention.

A component of a magnetization 237 and a component of a magnetization238 of the free layer 230 form a net magnetization of second layer 239,and the net magnetization of second layer 239 may form an included angleθ_(a) with the direction normal to the layers, namely, the netmagnetization of second layer 239 substantially perpendicular to thefree layer 230.

A spin-polarized current 240 drives through the magnetic random accessmemory 200 upward or downward as a read current or a write current,which makes the net magnetization of second layer 239 turn upward ordownward (i.e. the spin transfer effect). The orientation of spin 241has an included angle θ_(b) with the spin-polarized current 240, whichdetermines the critical current value.

Third Embodiment

Referring to FIG. 3 again, modified LLG equations (1) and (2) for thenet magnetization of second layer 239 formed by the component of amagnetization 237 and the component of a magnetization 238 are givenbelow, by taking the parameters into account in Table 1:

TABLE 1 (1)$M_{1} = {{\gamma_{1}M_{1} \times \left( {H_{1} + {hM}_{2}} \right)} - {{\alpha_{1}M_{1} \times {\overset{.}{\mu}}_{1}} \pm {\frac{\gamma_{1}\hslash}{eV}\frac{I_{e\; 1}g_{1}^{\pm}}{M_{1}}M_{1} \times \mu_{1} \times \mu_{3}}}}$(2)$M_{2} = {{\gamma_{2}M_{2} \times \left( {H_{2} + {hM}_{1}} \right)} - {{\alpha_{2}M_{2} \times {\overset{.}{\mu}}_{2}} \pm {\frac{\gamma_{2}\hslash}{eV}\frac{I_{e\; 2}g_{2}^{\pm}}{M_{2}}M_{2} \times \mu_{2} \times \mu_{3}}}}$Parameters Definitions of the parameters M₁ component of a magnetization237 M₂ component of a magnetization 238 M₁ magnetization magnitude of M₁M₂ magnetization magnitude of M₂ γ₁ gyromagnetic ratio of the componentof a magnetization 237 γ₂ gyromagnetic ratio of the component of amagnetization 238 H₁ net effective field of the component of amagnetization 237 H₂ net effective field of the component of amagnetization 238 hM₁ effective local exchange field of the component ofa magnetization 237 on the component of a magnetization 238 (where h ≦0) hM₂ effective local exchange field of the component of amagnetization 238 on the component of a magnetization 237 (where h ≦ 0)α₁ corresponding damping coefficient of γ₁ α₂ corresponding dampingcoefficient of γ₂ μ₁ unit vector of M₁ μ₂ unit vector of M₂ μ₃ unitvector of the net magnetization of first layer 213  reduced Planck'sconstant = h/2π e electron charge = 1.602 × 10⁻¹⁹ Coulomb V volume ofthe free layer 230 I_(e1) spin-polarized current of electron 1 (e1)I_(e2) spin-polarized current of electron 2 (e2) g₁ coefficient for thecomponent of a magnetization 237 which depends on polarization of theelectron 1 (e1) g₂ coefficient for the component of a magnetization 238which depends on polarization of the electron 2 (e2) ± positive ornegative, depending on the direction of the spin-polarized current

From modified LLG equations (1) and (2) above, an intermediate formula(3) can be obtained for strongly coupled multilayer ferrimagnets below,wherein the “eff” index of the formulas (3), (4), (5), (6) and (7) meansthe net effective value of each parameter:

$\begin{matrix}{\overset{.}{\mu} = {{\gamma_{eff}\mu \times H_{eff}} - {{\alpha_{eff}\mu \times \overset{.}{\mu}} \pm {a_{l\; {eff}}^{\pm}\mu \times \mu \times \mu_{3}}}}} & (3) \\{\gamma_{eff} = \frac{M_{1} - M_{2}}{{M_{1}/\gamma_{1}} - {M_{2}/\gamma_{2}}}} & (4) \\{\alpha_{eff} = \frac{{\alpha_{1}{M_{1}/\gamma_{1}}} + {\alpha_{2}{M_{2}/\gamma_{2}}}}{{M_{1}/\gamma_{1}} - {M_{2}/\gamma_{2}}}} & (5) \\{a_{l\; {eff}}^{\pm} = {\frac{\hslash}{eV}\frac{\left( {{I_{e\; 1}g_{1}^{\pm}} + {I_{e\; 2}g_{2}^{\pm}}} \right)}{\left( {{M_{1}/\gamma_{1}} - {M_{2}/\gamma_{2}}} \right)}}} & (6) \\{H_{eff} = \frac{{M_{1}H_{1}} - {M_{2}H_{2}}}{M_{1} - M_{2}}} & (7) \\{I_{{e\; 1},2} = {I + {2{{I\left( {1 + {\cos \; \theta_{1,2}}} \right)}/\left( {3 + {\cos \; \theta_{1,2}}} \right)}}}} & (8)\end{matrix}$

The θ_(1,2) of the formula (8) depends on the orientation of the spin241 with regard to orientation of the net magnetization of second layer239 formed by the component of a magnetization 237 and the component ofa magnetization 238.

Assuming μ₃=c, H_(eff)=H_(eff) c (C is a constant), and considering anantiparallel coupling effect between magnetic rare-earth (RE) andtransition-metal (TM) samples, the aforementioned intermediate formula(3) can be solved as follows:

{dot over (θ)}=±(a _(I) _(eff) ^(±)−ωα_(eff))sin θ  (9)

A resultant formula (9) allows obtaining the eight critical currentvalues of the spin-polarized current for different spin orientations,which present in the form of the formulas (10), (11) and (12) below:

$\begin{matrix}{I_{C}^{\pm {,a}} = \frac{\alpha_{eff}\omega \; {{eV}\left( {{M_{1}/\gamma_{1}} + {M_{2}/\gamma_{2}}} \right)}}{\left( {{2g_{1}^{\pm}} + g_{2}^{\pm}} \right)\hslash}} & (10) \\{I_{C}^{\pm {,b,d}} = {\frac{3}{5}\frac{\alpha_{eff}\omega \; {{eV}\left( {{M_{1}/\gamma_{1}} + {M_{2}/\gamma_{2}}} \right)}}{\left( {g_{1}^{\pm} + g_{2}^{\pm}} \right)\hslash}}} & (11) \\{I_{C}^{\pm {,c}} = \frac{\alpha_{eff}\omega \; {{eV}\left( {{M_{1}/\gamma_{1}} + {M_{2}/\gamma_{2}}} \right)}}{\left( {g_{1}^{\pm} + {2g_{2}^{\pm}}} \right)\hslash}} & (12)\end{matrix}$

Fourth Embodiment

Reference is made to FIGS. 4 a, 4 b, 4 c and 4 d, wherein there areeight spin orientation configurations of the spin-polarized currentapplied to the same magnetic memory device. The component of amagnetization and the net magnetization of the free layer may have aincluded angle θ with the perpendicular line and free to rotate.

For example, a Tb_(x)(FeCo)_(1-x) sample using M₁=2644 X_(R) emu/cm³ andM₂=799(1−X_(R)) emu/cm³, where X_(R) is atomic percentage of the REelement, a minimum value for both I_(c) ⁺ and I_(c) ⁻ when X_(R)=24% canbe found.

The I_(c) ^(+,i) and I_(c) ^(−,i) values are obtained (the result listedin Table 2 below) by using formulas (10), (11) and (12), which assume a60×130 nm² elliptical sample for a Tb_(x)(FeCo)_(1-x) ferrimagneticstructure. The parameters used in all the results mentioned are in Table3 below.

As the value of the spin orientation θ_(c) changes from 0 to π, thevalue of critical current Ic⁻ decreases; and the current density Jc⁺also decreases. Furthermore, when the value of the spin orientationθ_(c) changes from π to 0, the value of critical current Ic⁻ decreases;and the current density Jc⁺ also decreases continuously.

TABLE 2 Spin orientation Ic⁺ Jc⁺ Ic⁻ Jc⁻ (θ_(c)) (μA) (A/cm²) (μA)(A/cm²) 0 482.09 1.97 × 10⁶ −101.16 −4.13 × 10⁵ π/2 302.20 1.23 × 10⁶−120.37 −4.91 × 10⁵ π 257.59 1.05 × 10⁶ −197.27 −8.05 × 10⁵ 3π/2 302.21.23 × 10⁶ −120.37 −4.91 × 10⁵

TABLE 3 Rare-Earth Transition Metal M (emu/cm³) 634.56 607.24 γ (Hz/Oe)γ₁ = 1.0 × 10⁷ γ₂ = 2.5 × 10⁷ α (damping coefficient) α₁ = 0.25 α₂ = 0.5Ku (erg/cm³) Ku₁ = 1.5 × 10⁵ Ku₂ = 1.0 × 10⁵ P (the polarizing factor) 0.8  0.7

By the manner of deriving the modified LLG equations, the variationtendency of the critical current value can be confirmed by changing thespin orientation. After setting some boundary conditions, the estimationof the critical current is obtained.

According to the composition and the embodiments above, there are manyadvantages of the present invention over the prior art, such as:

1. The manufacturing processes and the structural layers of the magneticsystem of the present invention are fewer than those of the prior art,so the cost and yield of production are improved.

2. The material of the pinned layer and the free layer isperpendicularly anisotropic ferrimagnetic, which allows the volume of asingle magnetic system to be smaller than that of the prior art.

3. By the method of controlling the spin orientation of thespin-polarized current, the power consumption of the magnetic system canbe reduced via reducing critical current.

It will be apparent to those skilled in the art that variousmodifications and variations can be made to the structure of the presentinvention without departing from the scope or spirit of the invention.In view of the foregoing, it is intended that the present inventioncover modifications and variations of this invention provided they fallwithin the scope of the following claims and their equivalents.

1. A method for reducing critical current of a magnetic random accessmemory, comprising: using modified Landau-Lifshitz-Gilbert equations toderive an intermediate formula describes the dynamics of netmagnetization; calculating the dynamics of net magnetization by theintermediate formula under the influence of a spin-polarized current toderive a resultant formula, wherein the spin-polarized current isarranged to apply to the magnetic random access memory; and inputtingthe boundary conditions of the magnetic random access memory into theresultant formula to obtain a value of the critical current.
 2. Themethod of claim 1, wherein the modification of the modifiedLandau-Lifshitz-Gilbert equations is provided by involving effectiveparameters.
 3. The method of claim 1, wherein a value of the criticalcurrent is decreased by changing a spin orientation of thespin-polarized current.